CalDav Support
As of Zimbra 5.0 there is native CalDav support. The link below includes instructions on how to configure Zimbra CalDav for Apple iCal.
For information on using Thunderbird/Lightning with Zimbra visit Accessing_Zimbra_Collaboration_Suite_with_Thunderbird or Thunderbird & Lightning.
mod_dav support in tomcat would be a starting point:
http://tomcat.apache.org/connectors-doc-archive/jk2/jk2/davhowto.html